Finite Group Databasebeta

← C43×#25587 #24945604

Subgroups — C43×#25587 #24945604

Order 11008.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3505C211yesmaximal, characteristic, complemented
2C43×#2561C211yesmaximal, characteristic, complemented
3C43×#2539C211yesmaximal, characteristic, complemented
4C43×#2534C211yesmaximal, characteristic, complemented
5C43×#2022C212yesmaximal, complemented
6C43×#2021C212yesmaximal, complemented
7C43×#1996C211yesmaximal, characteristic, complemented
8C43×#1964C211yesmaximal, characteristic, complemented
9C43×#1890C212yesmaximal, complemented
10C43×#1889C212yesmaximal, complemented
11C4×#99×C43C211yesmaximal, characteristic, complemented
12C43×#553—22no—
13C43×#553—21no—
14C43×#552—21no—
15C43×#551—22no—
16C43×#548—21no—
17C43×#546—21no—
18C43×#539—21no—
19C43×#538—21no—
20C43×#534C2212yes—
21C43×#529—21no—
22C43×#525—21no—
23C2×#123×C43C2212yes—
24C2×#123×C43C2211yescharacteristic
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#120×C43C2212yes—
28C2×#120×C43C2211yescharacteristic
29C43×#518C2212yes—
30C2×C4×D4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C2×#99×C43C2212yes—
33C2×#99×C43C2212yes—
34C2×#99×C43C2212yes—
35C43×#399—21no—
36C43×#397—21no—
37C43×#396—21no—
38C43×#394—21no—
39C43×#393—21no—
40C43×#392—21no—
41C43×#390—22no—
42C43×#388—22no—
43C43×#388—21no—
44C43×#386—21no—
45C43×#381C2211yescharacteristic
46C43×#381C2212yes—
47C43×#380C2211yescharacteristic
48C43×#379C2211yescharacteristic
49C43×#379C2212yes—
50C4×C22⋊C4×C43C2211yescharacteristic
51C4×C22⋊C4×C43C2211yescharacteristic
52C43×#342C2212yes—
53C43×#342C2212yes—
54C43×#342C2212yes—
55C25×C43C2311yescharacteristic
56C2×#41×C43—21no—
57C22×Q8×C43D411yescharacteristic, complemented
58C22×D4×C43—21no—
59C22×D4×C43—22no—
60C22×D4×C43D411yescharacteristic, complemented
61C22×D4×C43C2311yescharacteristic
62C22×D4×C43C2312yes—
63C23×C4×C43D411yescharacteristic, complemented
64C23×C4×C43C2311yescharacteristic
65C23×C4×C43C2311yescharacteristic
66#126×C43—22no—
67#126×C43—22no—
68#126×C43—22no—
69#125×C43—21no—
70#125×C43—22no—
71#124×C43—21no—
72#124×C43—22no—
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—22no—
77#123×C43—22no—
78#123×C43—24no—
79#123×C43—42no—
80#123×C43—42no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87#121×C43—21no—
88#121×C43—22no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43—21no—
93#121×C43—22no—
94#121×C43—22no—
95#120×C43—22no—
96#120×C43—22no—
97#120×C43—24no—
98#120×C43—42no—
99#120×C43—42no—
100C4×Q8×C43—21no—
101C4×D4×C43—22no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111#117×C43—21no—
112#117×C43—22no—
113#117×C43—22no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43D411yescharacteristic, complemented
118C2×C4⋊C4×C43D411yescharacteristic, complemented
119C2×C4⋊C4×C43D412yescomplemented
120C2×C4⋊C4×C43D411yescharacteristic, complemented
121C2×C22⋊C4×C43—22no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—22no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—22no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43D411yescharacteristic, complemented
137C2×C22⋊C4×C43D412yescomplemented
138C2×C22⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43C2312yes—
141C2×C22⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43C2312yes—
143C2×C22⋊C4×C43C2312yes—
144C2×C42×C43—21no—
145C2×C42×C43—21no—
146C2×C42×C43D411yescharacteristic, complemented
147#99×C43—24no—
148#99×C43—42no—
149#99×C43—42no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154#95×C43—22no—
155#95×C43—21no—
156#95×C43—22no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—42no—
163C24×C43—81no—
164C24×C43C2×D412yes—
165C24×C43C2×D411yescharacteristic
166C24×C43C2411yescharacteristic
167#41×C43—82no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—81no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—22no—
177C2×D4×C43—21no—
178C2×D4×C43—22no—
179C2×D4×C43—22no—
180C2×D4×C43—22no—
181C2×D4×C43—22no—
182C2×D4×C43—22no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—44no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—44no—
189C2×D4×C43—81no—
190C2×D4×C43—81no—
191C2×D4×C43—82no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—22no—
197C22×C4×C43—21no—
198C22×C4×C43—22no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—81no—
206C22×C4×C43—81no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C4⋊C4×C43—22no—
220C4⋊C4×C43—22no—
221C4⋊C4×C43—22no—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—44no—
232C4⋊C4×C43—42no—
233C4⋊C4×C43—81no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—22no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—44no—
254C22⋊C4×C43—44no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—44no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—41no—
260C22⋊C4×C43—41no—
261C22⋊C4×C43—41no—
262C22⋊C4×C43—41no—
263C22⋊C4×C43—81no—
264C22⋊C4×C43—82no—
265C22⋊C4×C43#4114yescomplemented
266C42×C43—22no—
267C42×C43—22no—
268C42×C43—21no—
269C42×C43—21no—
270C42×C43—81no—
271C42×C43—81no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—84no—
300C23×C43—84no—
301C23×C43C22×D411yescharacteristic
302C23×C43C22×D411yescharacteristic
303C23×C43C22×D411yescharacteristic
304C23×C43C2×#4112yes—
305C23×C43H(5,𝔽2)12yes—
306Q8×C43—42no—
307Q8×C43—81no—
308D4×C43—42no—
309D4×C43—42no—
310D4×C43—42no—
311D4×C43—42no—
312D4×C43—42no—
313D4×C43—42no—
314D4×C43—42no—
315D4×C43—81no—
316D4×C43—82no—
317D4×C43—82no—
318D4×C43—88no—
319D4×C43—84no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—24no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—42no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
340C2×C4×C43—41no—
341C2×C4×C43—42no—
342C2×C4×C43—41no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43—41no—
346C2×C4×C43—42no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43—42no—
358C2×C4×C43—81no—
359C2×C4×C43—82no—
360C2×C4×C43—82no—
361C2×C4×C43#12011yescharacteristic
362C2×C4×C43#12011yescharacteristic
363C2×C4×C43#12011yescharacteristic
364C2×C4×C43#12011yescharacteristic
365#25587C4311yesmaximal, characteristic, direct product factor, Sylow
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—44no—
375C22×C43—42no—
376C22×C43—44no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—82no—
387C22×C43—81no—
388C22×C43—82no—
389C22×C43—82no—
390C22×C43—81no—
391C22×C43—82no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43C2×#12011yescharacteristic
396C22×C43#53211yescharacteristic
397C22×C43#53511yescharacteristic
398C22×C43#54612yes—
399C22×C43#55012yes—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—44no—
405C4×C43—41no—
406C4×C43—42no—
407C4×C43—41no—
408C4×C43—42no—
409C4×C43—41no—
410C4×C43—42no—
411C4×C43—81no—
412C4×C43—82no—
413C4×C43—81no—
414C4×C43—81no—
415#3505C2×C4311yescharacteristic, complemented
416#2561C2×C4311yescharacteristic, complemented
417#2539C2×C4311yescharacteristic, complemented
418#2534C2×C4311yescharacteristic, complemented
419#2022C2×C4312yescomplemented
420#2021C2×C4312yescomplemented
421#1996C2×C4311yescharacteristic, complemented
422#1964C2×C4311yescharacteristic, complemented
423#1890C2×C4312yescomplemented
424#1889C2×C4312yescomplemented
425C4×#99C2×C4311yescharacteristic, complemented
426C2×C43—22no—
427C2×C43—21no—
428C2×C43—22no—
429C2×C43—21no—
430C2×C43—82no—
431C2×C43—81no—
432C2×C43—82no—
433C2×C43#243111yescharacteristic
434C2×C43#302511yescharacteristic
435C2×C43#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C4312yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C4312yes—
448C2×#123C22×C4311yescharacteristic
449C2×C22⋊Q8C22×C4311yescharacteristic
450C2×#121C22×C4311yescharacteristic
451C2×#120C22×C4312yes—
452C2×#120C22×C4311yescharacteristic
453#518C22×C4312yes—
454C2×C4×D4C22×C4311yescharacteristic
455C22×C22⋊C4C22×C4311yescharacteristic
456C2×#99C22×C4312yes—
457C2×#99C22×C4312yes—
458C2×#99C22×C4312yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C4312yes—
470#381C22×C4311yescharacteristic
471#380C22×C4311yescharacteristic
472#379C22×C4312yes—
473#379C22×C4311yescharacteristic
474C4×C22⋊C4C22×C4311yescharacteristic
475C4×C22⋊C4C22×C4311yescharacteristic
476#342C22×C4312yes—
477#342C22×C4312yes—
478#342C22×C4312yes—
479C43#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C4311yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C4311yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C4311yescharacteristic, complemented
486C22×D4C23×C4311yescharacteristic
487C22×D4C23×C4312yes—
488C23×C4D4×C4311yescharacteristic, complemented
489C23×C4C23×C4311yescharacteristic
490C23×C4C23×C4311yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C4311yescharacteristic, complemented
543C2×C4⋊C4D4×C4311yescharacteristic, complemented
544C2×C4⋊C4D4×C4312yescomplemented
545C2×C4⋊C4D4×C4311yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C4311yescharacteristic, complemented
562C2×C22⋊C4D4×C4312yescomplemented
563C2×C22⋊C4C23×C4311yescharacteristic
564C2×C22⋊C4C23×C4311yescharacteristic
565C2×C22⋊C4C23×C4312yes—
566C2×C22⋊C4C23×C4311yescharacteristic
567C2×C22⋊C4C23×C4312yes—
568C2×C22⋊C4C23×C4312yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C4311yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C4312yes—
590C24C2×D4×C4311yescharacteristic
591C24C24×C4311yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C2×D4×C4312yes—
634C22×C4C2×D4×C4311yescharacteristic
635C22×C4C2×D4×C4312yes—
636C22×C4C2×D4×C4311yescharacteristic
637C22×C4C2×D4×C4312yes—
638C22×C4C2×D4×C4311yescharacteristic
639C22×C4C2×D4×C4311yescharacteristic
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C2×D4×C4311yescharacteristic
643C22×C4C2×D4×C4311yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C4314yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C4311yescharacteristic
727C23C22×D4×C4311yescharacteristic
728C23C22×D4×C4311yescharacteristic
729C23C2×#41×C4312yes—
730C23H(5,𝔽2)×C4312yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C4311yescharacteristic
787C2×C4#120×C4311yescharacteristic
788C2×C4#120×C4311yescharacteristic
789C2×C4#120×C4311yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C4311yescharacteristic
820C22C43×#53211yescharacteristic
821C22C43×#53511yescharacteristic
822C22C43×#54612yes—
823C22C43×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C43×#243111yescharacteristic
847C2C43×#302511yescharacteristic
848C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C43×#3505C2semidirect
2. C43×#2561C2semidirect
3. C43×#2539C2semidirect
4. C43×#2534C2semidirect
5. C43×#2022C2semidirect
6. C43×#2021C2semidirect
7. C43×#1996C2semidirect
8. C43×#1964C2semidirect
9. C43×#1890C2semidirect
10. C43×#1889C2semidirect
11. C4×#99×C43C2semidirect
57. C22×Q8×C43D4semidirect
60. C22×D4×C43D4semidirect
63. C23×C4×C43D4semidirect
117. C2×C4⋊C4×C43D4semidirect
118. C2×C4⋊C4×C43D4semidirect
119. C2×C4⋊C4×C43D4semidirect
120. C2×C4⋊C4×C43D4semidirect
136. C2×C22⋊C4×C43D4semidirect
137. C2×C22⋊C4×C43D4semidirect
146. C2×C42×C43D4semidirect
265. C22⋊C4×C43#41semidirect
365. #25587C43direct (N × H)
415. #3505C2×C43semidirect
416. #2561C2×C43semidirect
417. #2539C2×C43semidirect
418. #2534C2×C43semidirect
419. #2022C2×C43semidirect
420. #2021C2×C43semidirect
421. #1996C2×C43semidirect
422. #1964C2×C43semidirect
423. #1890C2×C43semidirect
424. #1889C2×C43semidirect
425. C4×#99C2×C43semidirect
479. C43#25587direct (N × H)
482. C22×Q8D4×C43semidirect
485. C22×D4D4×C43semidirect
488. C23×C4D4×C43semidirect
542. C2×C4⋊C4D4×C43semidirect
543. C2×C4⋊C4D4×C43semidirect
544. C2×C4⋊C4D4×C43semidirect
545. C2×C4⋊C4D4×C43semidirect
561. C2×C22⋊C4D4×C43semidirect
562. C2×C22⋊C4D4×C43semidirect
571. C2×C42D4×C43semidirect
690. C22⋊C4#41×C43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#35052
C43×#25612
C43×#25392
C43×#25342
C43×#20222
C43×#20212
C43×#19962
C43×#19642
C43×#18902
C43×#18892
C4×#99×C432
#2558743